Question
Answer
$$-3x^2(x-y^2)-(y^3-5)-3y^2(x^2-4y)+4x^3=x^3+11y^3+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3x^2(x-y^2)-(y^3-5)-3y^2(x^2-4y)+4x^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(3x^3-3x^2y^2)-(y^3-5)-(3x^2y^2-12y^3)+4x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-3x^3+3x^2y^2-(y^3-5)-(3x^2y^2-12y^3)+4x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-3x^3+3x^2y^2-y^3+5-(3x^2y^2-12y^3)+4x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-3x^3+3x^2y^2-y^3+5-3x^2y^2+12y^3+4x^3 \xlongequal{ } \\[1 em] & \xlongequal{ }-3x^3+ \cancel{3x^2y^2}-y^3+5 -\cancel{3x^2y^2}+12y^3+4x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^3+11y^3+5\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3x^2} $ by $ \left( x-y^2\right) $ $$ \color{blue}{3x^2} \cdot \left( x-y^2\right) = 3x^3-3x^2y^2 $$Multiply $ \color{blue}{3y^2} $ by $ \left( x^2-4y\right) $ $$ \color{blue}{3y^2} \cdot \left( x^2-4y\right) = 3x^2y^2-12y^3 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(3x^3-3x^2y^2 \right) = -3x^3+3x^2y^2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( y^3-5 \right) = -y^3+5 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x^2y^2-12y^3 \right) = -3x^2y^2+12y^3 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-3x^3} + \, \color{red}{ \cancel{3x^2y^2}} \, \color{orange}{-y^3} +5 \, \color{red}{ -\cancel{3x^2y^2}} \,+ \color{orange}{12y^3} + \color{blue}{4x^3} = \color{blue}{x^3} + \color{orange}{11y^3} +5 $$ |
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